The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A Mechanically Checked Proof of the AMD5K86TM Floating-Point Division Program
IEEE Transactions on Computers
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Verifying the Accuracy of Polynomial Approximations in HOL
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Generic Library for Floating-Point Numbers and Its Application to Exact Computing
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
More accuracy at fixed precision
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
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An additive symmetric value b of a with respect to c satisfies c = (a + b)/2. Existence and uniqueness of such b are basic properties in exact arithmetic that fail when a and b are floating point numbers and the computation of c performed in IEEE-754-like arithmetic. We exhibit and prove conditions on the existence, the uniqueness and the consistency of an additive symmetric value when b and c have the same sign.